What is `int x*e^(-x^2) dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find the value of : `int x*e^(-x^2) dx`

Let -x^2 = y

dy/dx = -2x

x*dx = (-1/2)*dy

`int x*e^(-x^2) dx`

=> `int (-1/2)*e^y dy`

=> `(-1/2)*e^y`

substitute y = -x^2

=> `-1/(2*e^(x^2))`

The required integral is `-1/(2*e^(x^2))`